A lop sided face, along with the head tilt, is an indication of a likely inner/middle ear infection. The infection puts pressure on the facial nerve, causing paralysis and one side of the face to droop. The antibiotics was the right treatment, but should have been given for an extended treatment period until the symptoms resolved (plus at least 2 weeks beyond), along with the anti inflammatory meloxicam (0.3-0.6mg/kg, 2x a day, dose recommended for rabbits). Typically 4-6 weeks minimum is needed, but this will depend on the antibiotic used and the type of bacteria present.
Medirabbit: ear infection clinical signs and treatment
At this point, with the infection worsening, more 'heavy duty' antibiotics may be needed, like pen g procaine/benzathine injections or azithromycin. Azithromycin can be an extremely effective antibiotic for ear infections when dosed correctly for rabbits (50mg/kg), though this also will depend if the bacteria involved is sensitive to it. It does work quickly (2-3 days to see significant improvement I found) and penetrates tissue and bone well, but some rabbits can have a very negative reaction to it causing severe digestive problems, so it can't always be used.
Scans or xrays are also helpful, to determine the exact nature of the infection, and if it's dental related. If it is dental related, at some point that will need to be dealt with as well, with possible tooth removal needed. This can be a long difficult illness and treatment to deal with, so be prepared.
I would suggest reading some of the references in these articles as well, as they contain a lot of helpful information. There's also a fb page called 'headtilt for hoppers' , I believe, with members that will have valuable information and insight to share based on their own experiences.
https://wabbitwiki.com/wiki/Otitis
https://wabbitwiki.com/wiki/Head_tilt
Treatment for ear infections usually needs to be aggressive, as they can be very difficult to treat and can spread if the infection isn't brought under control. If your vet isn't a knowledgeable rabbit vet, I would suggest finding the best rabbit vet you can, to take your rabbit to for treatment. I would direct you to the HRS rabbit vet list, but they've revamped their site and I can't seem to find the list now. So you may have to do some research if you're needing to find a better rabbit vet to go to.
https://rabbit.org/veterinarians/
There are a few other less common causes like a stroke, or a tumor, but an ear infection would be most likely. And seems likely based on the improvement you saw with the first antibiotic treatment.
The flaky skin could be mites, but is secondary and will need the necessary antiparasitic when the vet determines it's appropriate.